Quantum simulation kernels also appear in recently developed variational quantum algorithms, in which the vast majority of the program is an ansatz (parameterized quantum circuit). One popular type of ansatz with good trainability is the application-inspired ansatz [1]} which can be considered as a simulation kernel.
Compared with implementing \({\rm exp}({\rm i}H\Delta t)\) , the only difference is that the \(\Delta t\)  is changed to some tunable parameters associated with different Pauli strings and the overall program structure remains the same.
For example, Figure REF  (b) shows the ansatz of QAOA algorithm [2]} on a 4-node graph Max-Cut problem.
The graph of the problem has 5 edges of different weights, and the Hamiltonian of this problem is the weighted sum of the 5 Pauli strings associated with the 5 edges.
The majority of the QAOA ansatz [2]} is to implement the 5 operators on the right (\(\gamma \)  is the parameter).
